Fake Weighing

Algebra Level 2

Mrs. Johnson is a fishmonger at a wet market, and she uses a weighing balance to measure the weight of the wish that she buys and sells. When she bought a fish, she placed the fish in one pan, and balanced it against 3 weights which were labeled with 500 grams each in the other pan.

As she was cleaning the fish, she found that there was a piece of lead which weighs 300 grams inside the stomach. Furthermore, she misread one of her weights, and it was just 200 grams instead.

If the value of fish is $9.00 per kilogram, what is the loss of Mrs. Johnson?

Image credit: Wikipedia Visitor7
$5.40 $4.50 $2.00 $3.75

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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6 solutions

Akshay Sonu
Apr 17, 2014

Firstly the total weight weighed is 1500, then the loss in the weight is 600 grams, as the price per 1000 grams is 9$, so the price for 900 grams is 8.1$, Actually the Mrs. johnson must get $13.5. so the loss is $5.4 , said the Sherlock Holmes.

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Firstly the total weight weighed is 500 3, then the loss in the weight is 200 3 grams, as the price per 1000 grams is 9$, so the price for 900 grams is 8.1$, Actually the Mrs. johnson must get $13.5. so the loss is $5.4.

Muhammad Saif - 7 years, 1 month ago
Neil Delos Reyes
Apr 19, 2014

weight she lost = 300g + (500g-200g) = 600g

value of loss = (600g)($9/1000g) = [ $5.4 ]

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Aronas Nuresi
Apr 17, 2014

9 1000 ⋅ ( ( 3 ⋅ 500 − 300 − ( 500 − 200 ) ) − 3 ⋅ 500 ) = − $ 5.40 \frac{9}{1000}\cdot ((3\cdot 500-300-(500-200))-3\cdot 500)=-\$5.40

5 Helpful 0 Interesting 0 Brilliant 0 Confused

1500 g

9/1000 = 0.009 price of one Gr.

200*0.009 = 1.8

300*0.009 = 2.7 4.5 $ loss

Mohammed Zain - 7 years, 1 month ago

2.7 4.5 $ loss

Bilal Zai - 7 years, 1 month ago
Eka Kurniawan
Apr 17, 2014

She measured 3 weights of 500g each firstly, hence the total weight of fish is 1.5kg. Then she realized that one of the weight is only 200g, so it's only 1.2kg. She also found 300g of lead. Hence the actual mass of the fish is 0.9kg. The mass differences is 0.6kg. So the total loss is 0.6kg times $9 per kg = $5.4

Oh, yes. Please visit my note everybody here and the admin also https://brilliant.org/discussions/thread/i-shouldnt-be-wrong/ because the practice solutions is kinda having some troubles. This is one of them.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Devendra Marghade
Apr 17, 2014

Money spent for 1.5 Kg @ 9$/Kg= 13.5 $ Actual weight of fish=1500gm-[300 gm(due to difference in weight)+300gm(due to lead present)] =900gm=0.9 Kg Actual money was to be spent=0.9*0.9=8.1 $ So loss=13.5-8.1= 5.4 $

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Total weight loss = 300 gm (lead) + (500-200) gm (misreading) = 600 gm ----------------- 1000 gm cost $9.00 -------------- Therefore 600 gm cost $ 9*600/1000 = $ 5.40 -------------- Therefore total loss = $5.40 -------------

Suyash Mittal - 7 years, 1 month ago
Rajkumar Mogadati
Apr 24, 2014

total loss=300(waste in stomach)+300(she misread 500gms instead of 200gms)=600gms.If 1kg costs 9 dollars then 0.6kg(600gms) costs 0.6 * 9 $=5.40 $. Therefore total loss of money is 5.40$

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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